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The tunneling method applied to global optimization. (English) Zbl 0565.65036
Numerical optimization, Proc. SIAM Conf., Boulder/Colo. 1984, 213-244 (1985).
[For the entire collection see Zbl 0552.00011.]
The purpose of this paper is to give a state-of-the-art review of the tunneling method [see the authors, Lect. Notes Math. 909, 34-47 (1982; Zbl 0473.65038)] applied to programming problems for computing the global optimal solutions. The authors, taking as a guide line the historical development of the tunneling method, discuss its applications to unconstrained global optimization, stabilization of Newton’s method for a system of nonlinear equations and constrained global optimization. Computational experience on several test problems is recorded. It is shown that programming problems having from one to ten variables and from three to several thousands of local minima can be solved by using this method.
Reviewer: J.Parida

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming